Posts Tagged ‘expansion’

We have lost the relationship between Number and Form or Number and Magnitude as the Ancient Greeks called their Forms.

A few years ago a Revolution in Mathematics and Physics has started. This revolution is caused by Geometric Algebra.

In Geometric Algebra the Ancient Theories of Euclid and Pythagoras are reevaluated.

Numbers are Scalar (Quantum) Movements of Geometric Patterns and not Static Symbols of Abstractions that have nothing to do with our Reality.

Movements and not Forces are the Essence of Physics.

The basic rule Movement = Space/Time (v=s/t) shows that Time and Space are two Reciprocal 3D-Spaces. Our Senses Experience Space and not Time.

The Simple Rule N/N=1/1=1 balances the Duals of Space and Time. One Unit Step in Space is always Compensated by One Unit Step in Time.

Geometric Algebra has a strange relationship with Pascals Triangle. This Triangle, also called the Binomial Expansion, contains all the Possible Combinations of two Independent Variables. Our Universe is a Combination of Combinations exploring Every Possibility.

The last and perhaps most important Discovery in Mathematics called Bott Periodicity shows itself in Pascals Triangle.

Bott Periodicity proves that we live in a Cyclic Fractal Universe, the Wheel of Fortune, that is Rotating around the Void, the Empty Set. The Empty Set contains Every Thing that is Impossible in our Universe.

This blog is not a Scientific Article. I have tried to connect the Old Sciences and the New Sciences in my own Way.

It contains many links to Scientific Articles and even Courses in Geometric Algebra.

So if you want to Dig Deeper Nothing will Stop You.

About the One and the Dirac Delta Function

Every Thing was created out of No Thing, the Empty Set, ɸ, the Void, the Tao. The Empty Set contains 0 objects.

The Empty Set is not Empty. It contains Infinite (∞) Possibilities that are Impossible.

Every impossibility has a probability of 0 but the sum of all possibilities (1/∞=0) is always 1. In the beginning ∞/∞ =1 or ∞x0=1.

This relationship is represented by the Dirac Delta Function. It is used to simulate a Point Source of Energy (a Spike, an Explosion) in Physics.

The Delta is reprented by the Symbol Δ, a Triangle. The Delta is called Dalet in the Phoenican and Hebrew Alphabet. Daleth is the number 4 and means Door.

The original symbol of the Delta/Daleth contains two lines with a 90 Degree Angle. Two orthogonal lines create a Square or Plane.

The Dirac Delta Function is defined as a Square with an Area of 1, a Width of 1/n and a Height of n where n->∞.

The Dirac Delta Function is a Line with an Area of 1.

In the Beginning a Huge Explosion took place that created the Universe.

When we move from 2D to 1D, the Number Line, the Delta Function becomes the Set of the Numbers N/N =1.

The Tetraktys of Pythagoras

The Monad (1) of the Tetraktys of Pythagoras, the Top of the Triangle, was created by Dividing the One (1) by Itself without Diminishing itself. The Monad (1/1=1) is part of the 1D Delta Function.

Creation is an Expansion of the 1/1 into the N/N, adding 1/1 all the time, until ∞/∞ is reached. At that moment every Impossibility has been realized.

The Dirac Delta Pulse

To move Back to the Void and restore the Eternal Balance of the One, Dividing (Compression) has to be compensated by Multiplication (Expansion).

At the End of Time N/M and M/N have to find Balance in the N/N, move Back to 1/1, Unite in the 0 and become The Void (ɸ) again.

About the Strange Behavior of Numbers

The big problem of the Numbers is that they sometimes behave very differently from what we Expect them to do.

This Strange Behavior happens when we try to Reverse what we are doing.

It looks like the Expansion of the Universe of Numbers is Easy but the Contraction creates many Obstacles.

It all starts with the Natural Numbers (1,2,3,).

When we Reverse an Addition (Subtract) and move over the Line of the Void Negative Numbers appear. Together with the Natural Numbers they are called the Integers.

The same happens when we Reverse a Division and the Fractions (the Rational Numbers) (1/3, 7/9) suddenly pop up.

An Integer N is a Rational Number divided by 1 (N/1).

The Integers are the Multiples of 1, the Fractions are its Parts.

Numbers behave even stranger when we want to Reverse a Repeating Repeating Addition (Irrational Numbers) and want to calculate a Rational Power (2**1/2).

The Complex Numbers (or Imaginary Numbers), based on the Square Root of -1 called i, are a combination of the Negative Numbers and the Irrational Numbers.

Irrational Numbers ( the Pythagorean Theorem), Fractions (a Piece of the Cake) and Negative Numbers (a Debt) are part of our Reality but the Strange Number i represents something we cannot Imagine.

About the Duality and the Expansion of Space

In the beginning the only One who was in existence was the 1.

When the One divide itself again the number -1, the Complement of 1, came into existence.

1 and -1 are voided in the No Thing, the Empty Set, 0: -1 + 1 = 0.

The Two, the Duality, both started to Expand in Two Opposite Directions (<– and +->) both meeting in the ∞/∞. This expansion is what we call Space.

Space is a Combination of the Strings S(1,1,1,1,1,…) and -S = (-1,-,1,-,1,-1,…) where S+S=(0,0,0,0,0,0,…).

The Expansion pattern of Space is a Recursive Function S: S(N)=S(N-1)+1 in which + means concatenate (or add) the String “,1″.

An Addition X + Y is a concatenation of S(X) and S(Y). A Substraction X-Y is a concatenation of S(X) and -S(Y). In the last case all the corresponding combinations of 1 and -1 are voided. (1,1,1,1)-(1,1,1)=(0,0,0,1)=(1).

Multiplication XxY is Adding String S(Y) every time a “1″ of S(X ) is encountered: 111 x 11 = 11 11 11. Dividing X/Y is Subtracting S(X) every time a “1″ of S(Y) is encountered:.111 111 1/111=11 1/111. In the last example a Fraction 1/111 appears.

According to Euclid “A Ratio is a sort of relation in respect of size between two magnitudes of the same kind“.

A Magnitude is a Size: a property by which it can be compared as Larger or Smaller than other objects of the Same Kind. A Line has a Length, a Plane has an Area (Length x Width), a Solid a Volume (Length xWitdth x Height).

For the Greeks, the Numbers (Arithmoi) were the Positive Integers. The objects of Geometry: Points, Lines, Planes , were referred to as “Magnitudes” (Forms). They were not numbers, and had no numbers attached.

Ratio, was a Relationship between Forms and a Proportion was a relationship between the Part and the Whole (the Monad) of a Form.

Newton turned the Greek conception of Number completely on its head: “By Number we understand, not so much a Multitude of Unities, as the abstracted Ratio of any Quantity, to another Quantity of the same Kind, which we take for Unity”.

We now think of a Ratio as a Number obtained from other numbers by Division. A Proportion, for us, is a statement of equality between two “Ratio‐Numbers”.

This was not the thought pattern of the ancient Greeks. When Euclid states that the ratio of A to B is the same as the ratio of C to D, the letters A, B, C and D do not refer to numbers at all, but to segments or polygonal regions or some such magnitudes.

The Ratio of two geometric structures was determinated by fitting the Unit Parts of the first geometric Stucture into the Other.

An Example: The Tetraktys is a Triangle (A Monad) and contains 9 Triangles (a Monad). The 1x1x1-Triangle Δ, a Part of the Tetraktys, is Proportional to the Whole of the Tetraktys (T) and has a Ratio T/Δ = 3= Δ -> T = Δ (3) x Δ (3) = 9.

The Mathematics of Euclid is not a Mathematics of Numbers, but a Mathematics of Forms.

The symbols, relationships and manipulations have Physical or Geometric Objects as their referents.

You cannot work on this Mathematics without Knowing (and Seeing) the Objects that you are Working with.

About Hermann Grassman, David Hestenes and the Moving Line called Vector

In his time the most important mathematicians did not understand what he was talking about although many of them copied parts of his ideas and created their own restricted version. None of them saw the whole Grassmann was seeing.

When he was convinced nobody would believe him he became a linguist. He wrote books on German grammar, collected folk songs, and learned Sanskrit. His dictionary and his translation of the Rigveda were recognized among philologists.

Grassmann took over the heritage of Euclid and added, Motion, something Euclid was aware of but could not handle properly.

A Displacement or Bivector

Grassmann became aware of the fact your hand is moving when you draw a 2D Geometric Structure. He called the Moving Lines, that connect the Points, Displacements (“Strecke”).

The Trick of Grassmann was that he could transform every transformation on any geometrical structure into a very simple Algebra. Multi-Dimensional Geometric Structures could be Added, Multiplied and Divided.

The Greek Theory of Ratio and Proportion is now incorporated in the properties of Scalar and Vector multiplication.

Combining (Adding) Bivectors creates a Trivector

About a 100 years later David Hestenes improved the Theory of Grassmann by incorporating the Imaginary Numbers. In this way he united many until now highly disconnected fields of Mathematics that were created by the many mathematicians who copied parts of Grassmanns Heritage.

Grassmann did not pay much attention to the Complex Numbers until he heard of a young mathematician called William Kingdon Clifford (1845-1879).

Complex numbers are ,just like the Rationals (a/b), 2D-Numbers. A Complex number Z = a + ib where i**2=-1. Complex Numbers can be represented in Polar Coordinates: Z = R (cos(x) + i sin(x)) where R = SQRT(a**2 + b**2). R is the Radius, the Distance to the Center (0,0).

When you have defined a 2D-complex Number it is easy to define a 4-D-Complex Number called a Quaternion: Z = a + ib + jc + kd or a 8-D Complex Number called an Octonion.

William Rowan Hamilton, the inventor of the Quaternions, had big problems to find an interpretation of all the combinations i, j and k until he realized that i**2 =j**2 = k**2 = ijk=-1.

What Hamilton did not realize at that time was that he just like Grassmann had invented Vector Algebra and Geometric Algebra.

Quaternions are rotations in 4D-space

This all changed when William Kingdon Clifford united everything in his new Algebra. Clifford’s algebra is composed of elements which are Combinations of Grassman’s Multivectors.

It turns out if you use combinations of these elements to describe your geometric objects you can do the same things you did before (you still have 3 vector components).

In addition, you can have additional data in those other components that let you find distances and intersections (and a lot of other useful information) using simple and (computationally) cheap numerical operations.

The most important Insight of William Kingdom Clifford was that the Complex Numbers are not Numbers all.

The Sum of every level N of the Triangle is 2**N. This Number expresses the Number of Directions of the Geometric Structure of a Space with Dimension N.

A Point has 0 Direction, while a Line has 2 Directions, relative to its Center point, a Plane has 4 Directions, relative to its Center Point, and a Cube has 8 directions, relative to its Center point.

Mount Meru (Pascal's Triangle in Vedic Mathematics)

Pascal’s Triangle is also called the Binomial Expansion. This Expansion shows all the Combinations of two letters A and B in the function (A+B)**N. Level 1 of the Triangle is (A+B)**0 = 1 and level 2 is A x A + 2 A x B + B x B -> 1,2,1.

The Diagonals of Pascal’s Triangle contain the Geometric Number Systems (Triangular Numbers, Pyramid Numbers, Pentatonal Numbers, ..) and the Golden Spiral of the Fibonacci Numbers.

Pascal’s Triangle is a Repository of all the Possible Magnitudes and their Components.

The Normal Distribution shows that the first level of the Triangle (the Tetraktys) is much more probable than the last levels.

The first four Levels of the Triangle of Pascal contain the Tetraktys of Pythagoras.

The Tetraktys is an Ancient Vedic Mathematical Structure called the Sri Yantra, Meru Prastara or Mount Meru.

About Numbers, Operations and the Klein Bottle

The Complex Numbers are not “Numbers” (Scalars) at all.

They are “Operations” (Movements) that can be applied to Magnitudes (Geometries) and Magnitudes are Combinations of the Simple Building Blocks of the Tetraktys, Points and Lines.

The Tao of Ancient China was not for nothing represented by a Flow of Water. According to the Ancient Chinese Mathematicians Every Thing Moves. In the Beginning there was only Movement.

In the Beginning only the One was Moved but when the Duality was created the Two moved around each other never getting into contact to Avoid the Void.

When we look at the Numbers we now can see that they are the result of the Movements of the first Diagonal of Pascals Triangle, the 1′s (Points) or better the Powers of the One: 1 **N (where N is a Dimension).

Even in the most simple Number System, the Unary Number System, Concatenation is an Operation, An Algorithm.

The Mathematician John Conway recently invented a new Number System called the Surreal Numbers that contains Every Number you can Imagine.

The Surreal Numbers are created out of the Void (ɸ) by a simple Algorithm (Conway calls an Algorithm a Game) that describes Movements (Choices of Direction: Up, Down, Left, Right, ..) that help you to Navigate in the N-Dimensional Number Space.

The Ancient Chinese Mathematicians played the same Game with the Numbers.

Algorithms were already known for a very long time by the Ancient Vedic Mathematicians. They called them Yantra’s.

Sri Yantra

Geometry is concerned with the Static Forms of Lines and Points but there are many other more “Curved” forms that are the result of Rotating Expansion and Compression. These forms are researched by the modern version of Geometry called Topology.

The most interesting 4D Topological Structure is the Klein Bottle. The Klein Bottle is a combination of two Moebius Rings. It represents a Structure that is Closed in Itself.

It can be constructed by gluing both pairs of opposite edges of a Rectangle together giving one pair a Half-Twist. The Klein Bottle is highly related to the Ancient Art of Alchemy.

The movement of the Duality around the Void can be represented by a Moebius Ring the Symbol of Infinity ∞.

Later in this Blog we will see why the Number 8 is a Rotation of ∞ and the symbol of Number 8 is a combination of the symbol of the number 3 and its mirror.

First we will have a look at the Reciprocal Relation between Space and Time.

The Klein Bottle, The Universe Closed in Itself, the Basic Structure behind Alchemy.

Larson believed that the failure to recognize that Motion is the most basic physical constituent of the universe has handicapped the progress of the traditional study of physics, which focuses on Forces.

The definition of Motion stems from the Equation of Velocity, v = ds/dt.

Instead of depending upon the change of the location of an object to define an arbitrary “quantum” of space per “quantum” of time, such as miles per hour, or meters per second, the RST assumes that the observed universal passage, or progression, of time is one aspect of a universal motion that necessarily must be accompanied by a universal “passage,” or progression, of space.

The Units of Time fill up the Units of Space. Space and Time are Duals.

Space is not-Time and Time is not-Space. Time is Non-Local, Cyclic and represented by the Rotating Imaginary Numbers. Space is Local, Linear and Represented by the Scalar Numbers. Space is the Vacuum and the Nothing and Time is the non-vacuum, the Every Thing, the Solids represented by the Cube of Space.

The Cube of Space is the structure behind the Tetraktys but also behind the Book of Genesis.

Our Reality contains two Reciprocal 3D-structures related to Space and Time. Space and Time are related by the Simple Formula N/N=1/1=1, the Formula of Diracs Delta Function.

We are able to perceive the Real 3D-Structure of Space. The 3D-Structure of Time is Imaginary. It is situated in the Imaginary Number Space of i.

Larson’s Cube, the Geometric Representation of the Octonion.

Larson, a Self Thought Genius like Grassmann, developed Geometric Algebra without knowing anything about Geometric Algebra but he also invented String Theory long before String Theory was invented. The Mathematics of Larson is also the Mathematics of the Tetraktys of Pythagoras without even knowing anything about it.

The Periodic System of Larson

Larson was able to Calculate all the important Physical Numbers without any problem and was also able to Calculate Chemical Structures and Reactions.

About the Bott Periodicity

The fourth line of Pascals Triangle and the Tetraktys contains 8 Directions in the Four Geometric Dimensions: 0, 1, 2, and 3.

Mathematicians are intrigued with this number 8, because they find it popping up unexpectedly in advanced mathematics.

In fact, expanding the Binomial Expansion to 8 dimensions just creates an inverse copy of these first Four Dimensions, and then the pattern just repeats itself with a half-twist and back from there, ad infinitum.

As you can see in the Picture above the Fractal Pattern of 8 contains two kinds of Trinities/Triangles, an Upside and a Downside (Rotated by 180 Degrees) Triangle. When you Rotate by 180 Degrees the 1 becomes -1 and 1 + -1 =0 is the Void.

The Star of David, the Symbol of Human Center, the Heart Chakra.

The Multi Dimensional Rotations of the Octonions always Come Back to Square 1/1=1, the One and keep Rotating around the Center, the Nothing, Until Infinity.

The Magic Square was carried by a Turtle. The Turtle is the symbol of the Constellation Orion. Many Ancient Cultures claim that our Ancestors came from this constellation. The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos (Time).

The Duality of Fu Xi and his Sister, The Snake of the Kundalini contains 3.5 (7/2) Twists. 2x3.5 = 7. 7 = (-1,-2,-3,0,1,2,3).

According to Chinese Creation Myth the world started with 無極(wuji: nothingness), the Tao. Out of the Tao, the Egg of the Zero (0) and the Supreme Pure One (1) emerged. In the next step the Trinity (3), the Three Pure Ones, was created.

The Tao produced One; One produced Two; Two produced Three; Three produced All things (Lao Tsu,Tao Te Ching, 42).

The Sri Yantra contains 43 Triangels and is generated by the Bronze Mean.

The Trinity is represented by a Triangle. A combination of Two Triangels is a Square. The combination of Two (2) Triangels is also the Symbol of the Heart Chakra, the merge of Heaven, the Upper Triangel and Earth, the Lower Triangel.

The most complex Yantra (“machine”), the Sri Yantra, contains 43 Triangels. The Sri Yantra is determinated by the Bronze Mean. The Bronze Mean is a generalization of the Sequence of Fibonacci based on the Trinity. The Bronze Mean generates Quasi-Crystals and Penrose Tilings.

The Square is a combination of two Triangels. It is represented by the Star of David, the Symbol of the Heart Chakra.

The Lo Shu Magic Square not only shows the Connection between the Four Forces that came out of the Two Forces, Expansion and Compression, it also shows the connection between Heaven and Earth.

In the Magic Square of Lu Shu the Even Numbers (2,4,6,8 = 2 x (1,2,3,4 = 2×2)) are Black(Yang, Male). The Odd Numbers (1,3,5,7,9 = 3×3) are White (Yin, Female). The Sum of all the Numbers is 15 (3×5).

The Even Numbers are situated at the Corners of the Square.

When the numbers of each row are multiplied (8x1x6; 3x5x7; 4x9x2) they together total to 225 ((3×5)x(3×5)) — as do those of the columns (8x3x4; 1x5x9; 6x7x2).

The Magic Square is dominated by two numbers (2**1, 2**2, 2**3) and (3, 2×3, 3**2), It contains four Prime Numbers (1,3,5,7). It also contains the first Perfect Number 6 (1+2+3 =1x2x3). 6 is also a Harmonic Divisor Number and has a Harmonic Divisor 2. The Sixth Day in the week is the day of Saturn, the God of Time.

The sequence 1,2,4,8, 1, 3,6,9, 27 is called theTetrad of the Pythagorians and was, according to Plato, used by the Demiurg, the Creator of our Universe, to create the Soul. The Soul is a mixture of the Same (1), the Different (2), and Existence (3). The Tetrad was used to define the Harmony of the Spheres.

When you connect the numbers of the Lo Shu a pattern appears that is called the Seal of Saturn or the Dance of Yu.

The Seal of Saturn or the Dance of Yu

The Sum of Magic Squares is a Magic Square and the product of a Magic Square M with a number a is again a Magic Square aM. Both Rules can be used to construct a Magic Square out of simple Binary Squares called Magic Carpets. One of these Magic Carpets is the Identity Matrix with One on the Diagonal.

Every Magic Square is related by Rotation and Mirroring to Eight other Magic Squares. This means that the central Lo Shu Magic Square with the Five in the Middle is related to Eight other Magic Squares with the other Numbers in the Middle. One of them contains the Nine and is called the Well.

The Lo Shu and the Well

The Sum of numbers of the Well is 18 (2×9) and the sum of all opposites across the 8 Spoke Wheel = 9 (9+0, 8+1, 7+2, 6+3, 5+4). 2×9 means that there are Two Complementary Magic Squares. One Magic Square is Rotating with the Clock and the other Against the Clock.

The Well is an Expansion and Contraction Cycle based on Powers of 2.

The Nine is the most important Number in the Magic Square. The Nine comes back in many ancient mythologies like the Egyptian Pesedjet and the Greek Ennead.

When you add the separate numbers of a number (54 = 5+ 4 = 9) the result is the Remainder when you divide the number by 9. This number is called the Modulo 9 number.

The Expansion and Compression Pattern shows that the same pattern repeats itself when the Magic Square is expanded or compressed Six (6) Times. The 7th Step is the Same as the First Step.

After 2**6=64 (8×8) divisons of the cell a Specialized Cell is created, the stem cell. The same happens in Music. The Game of Chess (Chiu King in China) with its 8×8 = 64 = 2**6 Playing Board contains every possible situation of the Game of Life.

The Two-Pattern does not contain the numbers 3,6 and 9. The number 9 is repeated every time when the pattern is expanded and compressed which means that Nine is the same as the Identity, the One (1+9 = 1). 3 and 6 Oscillate (1x2x3=6 and 1+2+3 =6) and therefore represent the Duality (3+6 = 9, = the One).

If we combine the Expansion and Compression patterns a Torus (a Rotating Circle, The Wheel of Time) appears. The Zero (the Void) is in the Center and Contains the Vortex. The Vortex represents another Cycle (Black/White Hole, 3,6,9, the Wheel of Order) in which every structure/pattern is destroyed to start All Over Again.

Lo Shu Torus

If we subtract the numbers in the Square by the number of the Center, 5, a highly Symmetric Pattern emerges. This pattern shows that there are Two Mirror Universes both containing four Forces.

When we transform this pattern from Modulus 9 to Modulus 3 (the Trinity) we see that the number 4 equals 1 and represents a new beginning of the Cycle.

4

9

2

-5

-1

4

-3

3

5

7

-5

-2

0

2

8

1

6

-5

3

-4

1

The Magic Square with the Zero in the Middle is surrounded by two Sequences of 123(4) with different Signs. The Signs are arranged in a Cyclic Pattern (- -, + -, + +, – +) that contains the Four Permutations of – and +. The Sum of the ++ and the — is -3 and +3, the Trinity. The Sum of +- en -+ is the One.

The Cyclic Pattern of + and – represents the Prisoners Dilemma that is solved by the Strategy of Tit for Tat. This strategy is applied by the Trickster, the God of Paradox, a concept of God in which God creates games that create games.

When you use the basic Addition and Multiplcation Rules of the Magic Square many important numbers and patterns appear that are related to Ancient Calenders, Symbols and Cycles.

About the Sum of Things

The Lo Shu Magic Square appeared a few years ago when I wanted to know more about Acupuncture. Acupuncture is related to the Sheng Cycle and the Sheng Cycle is related to the Lo Shu. A Magic Square is the perfect way to visualize the Constraints that control the Four Forces in our Universe.

Soon after this discovery I found out the Lo Shu is related to the Trinity and the Bronze Mean which is an abstraction of the Fibonacci Sequence. The Bronze Mean generates the Sri Yantra and so called Quasi Crystals. Quasi Crystals explain Acupuncture.

Ancient Alphabets are related to Numbers and Tones so Ancient Texts also represent Numerical Patterns and Music. You want be surprised to read that the Lo Shu showed itself in every Text Kim Veltman has analysed.

His document started a new inquiry into the pattern of the Lo Shu. During this research I detected the book “the Sum of Things” by Paul Martyn-Smith. Paul Martin-Smith worked together with Lee Burton.

This blog contains just a litte bit of the tremendous amount of information Paul Martin-Smith & Lee Burton have found about the essence of the I Tjing which is contained in just one simple 3×3 Magic Square.

If you want to know more the only thing you can do is to buy this book and start reading.

A model of a model is called a meta-model. Meta-models are made to increase the efficiency of the software-development process. You can go on with the creation of models-of-models (a meta-meta-model).

If there is nothing to stop you to model the model there is something wrong with the modeling approach.

When you are modeling you are compressing data. When you compress data the amount of data is reduced. A compression of a compression amounts to less data so there must be an end to the process of meta-modeling.

The counterpart of Compression is Expansion. When you have used a valid meta-modeling approach the meta-model has to expand to the original model without losing data.

When you want to make a meta-model you can model a static (a database) or a dynamic model (a process). Most of the meta-models of dynamic models are static models. They are stored in a database (dictionary, repository). The process of meta-modeling has the tendency to freeze the dynamics of a dynamic model.

A database is a combination of a storage-system and a software-program that stores and retrieves the data at the right place. A storage-system is also a software-program connected to a rotating device, a disk-drive, which is also managed by a software-program.

In reality every thing moves. Meta-Modeling splits a Dynamic System in a Database (a Datamodel) and Software (a Process) to Apply the Meta-Model. The Software is used to Expand the Compression of the Dynamic Model.

If you want to evaluate the efficiency of a meta-modeling approach you have look at the efficiency of the compression and the expansion of the data and the process.

When everything is a process, a method is a dynamic meta-model of a process. The meta-model of a method, a meta-meta-process, is a summary of the method. If you are not able to use the summary something is wrong with the method. If the summary is sufficient the real method is too complex.

The only way to create an efficient and reliable meta-model of a process is to find the self-similarity of the process. A self-reference, a fractal, of a process always contains less data and it is possible to enfold the fractal to a lower level without losing data.

If you use the fractal approach meta-meta-meta-….modeling is not needed because a fractal meta-model contains two parts, the fractal and the program to expand or compress the fractal to a lower or higher level.

Fractal compression and expansion is very successful in the area of image processing and textual summaries.

Is it possible to find the meta-model fractal?

The big problem is language. We express our reality in language and our current language is heavily distorted. It contains many interrelated overlapping layers.

If we use the language that is produced to describe processes we will perhaps be able to summarize, find the essence of the text, but we are never sure the text contains the real processes.

The solution to this problem is to observe processes and make a picture. If we Observe processes, look with the Eyes, we are producing Images. Fractal compression is able to compress these images.

How about the Ancient Scientists?

The ancient scientists were aware of the divine fractal. In my blog “About the Whole and the Parts” I use the Ternary Numbers or the Trinity to define a Meta-Model. The model starts with the Dynamic Whole and is expanded until it has replicated itself.

Interesting enough the theory behind fractal compression uses iterated functions based on the so called Sierpinski Gasket to detect fractals. The Sierpinski Gasket is an expansion of Triangles in Triangles. It is used to simulate DNA, a Biological Meta-Model and other “natural” structures

What happened?

The first expansion: Ø → 0. The Void, the Infinite Potential, transformed into the Nothing.

The second expansion: 0 →(-1,0,1). The nothing expanded in a negative and a positive part. The sum of the expansion is still zero. This is the principle of voiding. Every part that is created needs a counter-part that is it’s opposite (Part ∩ Counterpart = Ø). Every Expansion is compensated with the same Compression. When we divide a Whole we always have to make a “clear” cut (no overlap).

The third expansion: (-1,0,1) → (-2,-1,0),(0), (0,1,2). This is the creation of the Four Forces with the Void, the Zero (now the Fifth, Quintessence), in the Middle. Two of the Four Forces are the Same Forces that were formed in the Second Expansion. They could be called Expanding Expansion (Desire) and Compressing Compression (Control). The other two combinations are Expanding Compression and Compressing Expansion. Most of the time they are called Spirit (Creating) and Soul (Connecting). In the third expansion the Divine Fractal has expanded in Itself. That’s why we, the Humans, are created in the Image of God, the Creator.

Is it possible to transform the “divine” metamodel into a “normal” metamodel?

The whole problem comes down to language again. Are we able to translate the numbers into the Right Words? Let’s have a try.

0 or 5 are mostly called consciousness or the observer. In the terminology of IT 0 or 5 could be called a Monitor. The Monitor has to take care that every part has a counter-part.

1 and -1 are called Control and Desire. In terms of IT they could be called Rules and Sensors. The Sensors and the Rules are opposites. The Facts of the Sensors always fight the Structures (Methods, Systems, Programs) of the Rule-System. The conflict between Facts and Rules (Testing the Model) is the basic conflict behind every Scientific Approach.

-2 and +2 are called the Creator, the Imagination (Ideas) and the Emotions (Social Relationships). They represent the Possibility (in terms of new combinations of the existing Parts) to Enfold the model to a New level and the Role of the Human, the Actor, in the Game (defined by the Rules) that the Controller is playing with the Sensors. The Creator and the Emotions are also opposites. The Creator Splits and the Emotions Merge.

What is the fractal?

The Fractal is a Spiraling Spiral that moves Three Cycles Up and Three Cycles Down and rests in the Middle (the Seventh Day).

In the Cycle the Controller, the Sensors, Spirit and Soul are connected in Twelve possible ways.

Sometimes Spirit & Soul and Control & Desire void each other. It this case the Spiral moves back to the Void.

When Soul, Spirit and Desire (The Mother), the Female Trinity, are connected the Spiral Expands.

When Soul, Spirit and Control (The Father), the Male Trinity are connected the Spiral Compresses.

Spirit moves the Spiral Up and starts a new Level of Awareness.

Soul moves the Spiral Down to an existing Level of Communion.

The Divine Rule, the Golden Mean, the principle of Harmony, controls the Trinities of the Golden Spiral, to make sure that the spiraling spiral always voids itself in the end and returns to the Beginning.

The first fully programmable computer was Designed by Charles Babbage in 1837. Babbage failed to get enough money to Build his Analytical Engine. It was never build.

The failure of Charles Babbage delayed the creation of the current computer for about a 100 years.

Nobody knows that Thomas Fowler Designed and Implemented a completely different and simple wooden computer in 1840. The big difference between Babbage and Fowler was the Number System. Babbage used Base 10. Fowler used the Balanced Ternary Number System.

About the Ternary Number Systems

The balanced ternary number system is created by balancing Ternary (Base 3) Numbers around the Centre of the Number Line, 0. A balanced ternary number is a combination of negative and positive ternary numbers.

The balanced ternary number system is a very special Number System because all the basic mathematical operations, addition, subtracting, multiplication and division are accomplished by the application of very simple operations based on very special symmetries.

Symmetries are the foundation of Simplicity, Beauty and Elegance. The Engine of Fowler was a very simple and beautiful machine made out of wood.

When you want to represent a number you can start with base 1. The number 13 is represented by thirteen “1′s, “1111111111111″.

Of course you are free to use other symbols to represent the number “1″. When you want to represent 13 goats you could use 13 goat-like symbols. When you want to represent many goats the sequence of goat-like symbols becomes very long.

The next step is to group the goat-like numbers. You could group them in binary groups (11 11 11 11 11 11 1), ternary groups (111 111 111 111 1) or in every other group you want.

In every case you have to assign new symbols like “1″ → “-”, “11″→ “=” and “111″ → “≡”. The number 13 becomes “≡ ≡ ≡ ≡ -”.

When you have defined a grouping method you can repeat this method. The only thing you need is a new symbol “x” to represent repetition, a symbol that represents addition “+”, a rule how to read the sequence (left to right, right to left) and symbols (“(,”)”) that show what has to be combined. ≡ x (≡) + ≡ + – now means 3X3 + 3 + 1 = 13 (and not 3x(3+1 +1) = 21).

If you want to use a high base number you need many symbols to represent the numbers of the group. If you use a low base number you need many symbols to represent the repetition. An obvious strategy is to minimize the product of these two quantities. The result of this calculation is the number 3 (or better the number e)!

About Ternary Memory Systems

The number 3 is the most efficient way to represent numbers. There is much more to say about the properties of the number 3. One of these properties can be used in Databases and Storage systems.

A Balanced Ternary Storage system can be easily expanded because you can always add a new entrance in the middle. The Balanced Ternary Storage System (represented by the Arabic Mystical Lote Tree) is one of the simplest and efficient storing methods of data.

What is the reason behind this Blog?

The Universe is a highly complicated Knot

I am writing this blog because I have spent a lot of time to research the Scientific and Spiritual Trinity. The mathematical and the spiritual theory about the Trinity have a lot in common.

The Trinity or the Ternary Number System is the most efficient, most effective and most beautiful (in terms of symmetries) way to Represent, Calculate and Store Numbers. The Trinity is therefore the most effective Way to Represent the Fractal Expansion of the Dynamic Whole.

What happened?

The beginning of the Universe is a transformation of the Void (Ø) into the Nothing (0).

In the next step, the Egg of the 0 became the One (1) that splitted into the Duality (2) to become Aware of Itself.

In this case the first sequence of creation becomes Ø,0,1,2.

When we rewrite this sentence in balanced ternary language we read something else. In this case the beginning of the Universe is an expansion of the Void (0) into a negative (-1) and a positive part (1). The first sequence of creation becomes Ø (zero members of the set), (-1,0,1)(3 members of the set).

In the ternary balanced language the next expansion of the Universe is created by expanding the negative and positive part of the Universe in the Middle. A new expansion is created by adding the same structure in the Middle of the Middle of the Middle.

1

Ø

2

-1

0

1

-1

0

1

-1

0

1

3

-2

-1

-0

0

+0

1

2

This expansion moves on until the system has replicated itself. At that time the expansion moves faster and faster and faster. The Self-Referencing System of the Universe, the “Divine Fractal“, is unfolding itself at an ever increasing (logaritmic) speed in a spiraling spiral pattern creating many more (negative and positive) Numbers.

At a certain point the Negative and Positive numbers are Voided in the Zero and the Universe starts to expand again.

The unfolding creates many universes and one of these Universes is our own Universe. All the time the center, the 0, the Void, stayed at the middle.

At this moment the lowest level, our level, is almost finished and a new Evolution, a Jump to a new Level, has to start. This Jump will be a Jump out of the middle, the Heart Chakra.

Is this Explanation too Simple?

This explanation is much too simple because the whole creation process is now projected into one dimension, a Line, and we are looking at the third step of the Fourty-Two (3×13+4) Steps that have happened until now.

The basic structure of the Material Universe, the World Clock of Wolfgang Pauli, carried by the Demiurg, The Trickster.

Every split of the universe creates a new dimension. The splitted parts of the Universe, the balanced ternary trees, are Rotating Structures that contain Rotating Structures.

The other complication is that the Universe is creating its own Space and is therefore closed in itself. There is no Outside of the Universe. We are not living Inside an expanding Balloon but are travelling the Inside Surface.

When the Universe has expanded for a very long time the many dimensions are still there but they show themselves in very complicated Topological Structures like (Celtic) Knots, connected Moebius Rings, the Symbol of Infinity and the Klein Bottle, the Basic Structure behind Alchemy.

It is simply impossible to show and understand the current complexity. The only thing that is very helpful is to realize that the structure behind the Universe is a Fractal.

The Balanced Ternary Tree of 43.

This means that that at every level the same structure repeats itself. When you know everything there is to know about One Level you know every thing there is to know about Every Level.

If You understand the Human Being, You understand the Universe. This principle was called by the Ancient Scientists, “So Above, So Below” and “As Within, So Without”.

The Balanced Ternary Number System or the Trinity that contains the Trinity can be used to explain Your Self.

It can be used to explain the “strange” behavior of the Brain Trinity, a combination of a Whole, the Body, A Left and a Right Brain. The “Trinity Pattern” repeats itself in every part of your body.

The pattern of Seven (The Trinity in the Trinity) shows itself as the Seven Chakra’s. The next step, the Thirteen (3×4 +1 = 13), shows itself in the Twelve Signs of the Zodiac (+ the Center, the Pole Star), the Twelve Apostles (+ Jesus) and the Twelve Knight of Arthur (+Arthur).

The Expansion of this pattern on a much deeper level also generates the Acupuncture Points (Nadi’s) in Your Body.

Why is Science not Aware of this?

The main reason can be found in the story of Thomas Fowler. He invented a Very Simple computer system but he was beaten by the Complicated system of Charles Babbage.

Babbage used the 10 base to define his Engine and he needed lots of money to create this very complicated system. He never finished his analytical engine but many years later IBM almost copied his design when they developed the IBM 360. They were, like Microsoft, experts in Marketing. They sold what the Customer wanted to buy and never took time to think about the Essence.

The Klein Bottle, The Universe Closed in Itself, the Basic Structure behind Alchemy.

Thomas Fowler was a very simple man. He tried to do his best and was never aware of the power structures that controlled science and the market at that time. He wanted to help people but helping people is the stupidest thing you can do in a capitalistic system.

When an infrastructure is chosen it is almost impossible to change the infrastructure because everything that is build on top of this infrastructure becomes obsolete when the foundation is wrong. We will never be able to introduce a ternary computer infrastructure unless something happens that breaks the upper layer. Some people think this time is near.

Simplicity, Elegance, Beauty and Efficiency are not the main object of Capitalism. The main object of Capitalism is Making Profit.

What is the best Way to acquire Scientific Knowledge?

Thomas Fowler was not educated in the science of his time. He just invented the mathematics he needed. When he was educated in the science of his time he could have invented the same machine but it is much more plausible that he would have invented another Analytical Engine.

Thomas Fowler used his own judgment and his own talent to create something he thought was useful to support his own banking system (he also created a Bank!).

The Balanced Ternary Database of the Universe was called the Akasha. According to the Ancient Scientists of India every memory of the past and the future is stored in the Universe. They believed we are part of a Super Mind and this Mind knows everything that has happened or will happen.

The Vortex, a Painting of Walter Russell

Some people are suddenly connected to this Super Mind. They are Enlightened and find a solution for a very complicated problem in a Dream or a Trance State.

Strangely enough all of them receive or have received the same information.

What is going to happen?

The expansion of our Universe is getting into a critical state. This state is visible in all the fractal levels of our Universe.

It is visible in the Weather System, The Ecological System, The Economic System and the Cultural System. All of them are changing.

It is also visible in many Human Beings who experience the intervention of the Super-Mind in their Lives.

The big transformation must be visible in the Seven, until now not-connected universes. The other universes are currently shielded behind a Veil but this veil is slowly lifting. The movement of the Veil could explain the huge increase of Strange Encounters with Extraterrestials.

Our universe has been expanding and but very soon it will or may appear to stop. Our Universe may even begin to appear to shrink but it is not because it is reversing, heading towards some kind of big crunch but because it is folding, connecting to Itself, the Super Mind.

In the first stages of the Universe the Light was created but now we are entering a new phase where the consciousness of the Super Mind, is opening up to all the inhabitants of all the Seven Universes.

The opening of the Super Mind to all the Souls of the Universe has been named with many names in many religions all over the World (Ascension, the Golden Age, Point Omega, The Last Judgment, the Fifth World, The End of Time).

It is not clear what the connection with the Super Mind will accomplish. Many inspired scientists and prophets have tried to describe and explain this state.

One thing is sure it will be very different from the current situation where we are all isolated souls existing in many disconnected time-lines in many disconnected universes.

Economic Cycles move Up and Down. We are now in a Down-state, a Recession. To stimulate consumers the Central Banks lower the interest and are pumping a tremendous amount of money into the economy.

Pumping money generates inflation and when inflation happens prices start to rise again. What the economist wants to avoid is deflation.

When prices rise people will buy goods and invest money. When the prices go up you can make a profit. When prices rise you have to buy the goods on the short term because they will be much more expensive in the future. When consumers believe the economy will contract they will start to save money to cope with the problems they believe they will encounter in the future. They will also postpone the buying of (luxury) goods. When they postpone producers will lower their prices and when prices are lowered other prices will be lowered. This is called Deflation and Economists are terribly afraid Deflation will happen.

A state of contraction is just like a state of expansion highly related to Expectations and Expectations are a Self-Fulfilling Prophesy. If the self-fulfilling prophesy of a down-fall is not broken the economy will shrink until eternity. To motivate consumers to believe in an Expanding Economy Economists tell scientific fairy-tales hoping people will start to believe things are going the right way again.

Social scientists know for a long time that the majority of the people are not rational at all. Humans act on impulse and explain their behavior later. Humans believe others who believe others who believe others. Most of the things that are happening in the Economy are very complex and we need a simple explanation of a trusted expert. At this moment there is one thing everybody believes. Things are going in the wrong direction and One Thing is for Sure.

Bad news travel very fast.

The current state of technology has speeded up the transport of bad news to almost the speed of light. The contraction of the current economy moves much faster than the comparable contraction during the Great Depression.

The economy is controlled by two variables, Production and Consumption.

In a balanced economy the two variables are voided. The consumer destroys (consumes, eats) the products of the producer. The destruction of the product starts a new production-cycle. When the production is not voided producers have to create an inventory and take stock or speed up production. Producers don’t like to take stock. Stock costs a lot of Money.

Producers are just like Consumers highly controlled by their Expectation of the Future. The big difference between the two is the reaction-time. Consumers are able to Act on Impulse. It takes a lot of time and coordination to produce. Producers have to control their impulsive emotions but to sell their products they have to stimulate the impulses of their customers.

In the current economy the time between production and destruction is extremely shortened. To keep the customer satisfied new versions of products are produced almost on-demand (on impulse). To organize a demand-driven production-line the producer needs highly advanced logistic systems. One of the most important concepts of logistics is to optimize the Inventory. Inventory costs money and space. To produce a product the chains of suppliers are heavily integrated.

Nobody is taking stock and one disturbance in the production chain causes a disturbance in the complete chain. When the impulses of the consumers are suddenly stopped a complete chain slows down and production has to stop.

When the Banks are not able to finance a slowdown of the supply-chain the production has to stop even faster. Again the effect of bad news has a huge and fast impact on every producer in the world. At this moment all the interconnected wordwide supply-chains are collapsing

We are living in a time where negative impacts propagate with the Speed of Light. The political institutions are unable to react to the speed of change that is now changing the world in an instant.

People remember negative impacts much better than positive impacts. The expectation of the Human is constructed to avoid big trouble. The constant sequence of bad news lowers the trust in almost everything that was trusted before.

At this moment Advisors, Bankers, Politicians, the Stock exchange, the Banking System, the Political system, the Medical System, Pension Funds, Insurers, the World Economy, the Climate and much more are not Trusted anymore. Everything is interpreted out of a negative perspective. Not only the economy is contracting but also the trust in the now and the future is contracting. Not only the Economy is in a Depression, many people are Depressed.

Production and Consumption are two important variables but there are really five variables at stake.

The cycle of Expansion and Contraction is balanced by two other variable called Spirit and Soul. Soul is related to the Human Emotions. Spirit is related to Human Creativity. The Four variables move around a Center and this Center is moving around other Centers.

Spirit is the Creator of New Ideas. Ideas want to move Down. They want to be realized on Earth. It is very difficult to determine these ideas because Old Ideas want to be Replicated all the time. Old Ideas have to be destroyed to make place for the New ones. The only way to do this is to enforce Stress on the old replication-system. It is very clear that this is happening at this moment. The old solutions don’t work anymore.

Soul contains the Human Potential and this potential is basically unlimited. When the Soul is Stressed it Explodes and new Opportunities become visible. There are two types of Stress. The Stress to create something New, the Stress of the Artist who is desperately trying to Express something that is there but cannot be Grasped. The other type of Stress is caused by the constant pressure of something that is forcing the Human to do what he really don’t wants to do or is not capable of doing. Let us call this type of stress, Negative stress.

Soul and Spirit are connected to the Destructor and the Controller.

When the Negative Stressed Emotions connect to The Destroyer of the Senses the Human becomes Violent. Sadly enough the Destructive force of a World Wide War will certainly generate an Up-state of the Economy.

When the Negative Stressed Emotions connect to the Expectations of the Controller it will generate Fear. Fear is the Destructor of the Senses. It narrows the view of the Human and produces the simple insight of the Common Enemy. They (not we) are the cause of all evil. A long time ago the Jews were the scapegoat. Recently Islamic Terrorists were the most important enemy. At this moment the “Greedy Bankers”, the Capitalists are the cause of the big economic crisis. If we don’t watch out we are moving into a new Struggle of the Classes.

When people are Afraid they simply stop moving. They wait and see and start to look for protection. In this case Big Brother is always there to help them. Extreme fear generates the need for all kinds of weapons to prevent war and to stop or even destroy the Agressive Humans. The Stressed Emotions create Enemies, Protectors, Weapons and finally the perfect reason to Fight a War or start a Revolution. If we don’t watch out a Huge Violent Conflict is unavoidable.

When the Emotions connect to Spirit, Spirit will generate an Insight. When this Insight has appeared Spirit will Transform the Soul and the Human will be lifted to another Center, a new Frame of Reference, a new View on the outside World. In this case Spirit gives the Expectation Hope, a view on a Bright and Exciting Future. The Creative Spirit is the Powerful Force behind Enthusiasm and Motivation.

We are living in an Illusion. Money is an illusion, the Economy is an Illusion, The Banking System is an Illusion, and the Contraction of the Economy is an Illusion. If we keep on believing this Illusion, the Economy, will slowdown, until it finally stops. At that time we have to cooperate to survive.

We See what we want to see and when we See a Contraction, the Contraction will happen. Our Expectation creates the world it wants to see and when the Expectation is without Hope, the outside world becomes Hopeless.

We, the Humans, are perfectly capable to create a completely balanced economy if we listen to the other, exchange ideas, cooperate and start to implement the ideas. We will always make mistakes but mistakes generate new ideas and the cycle of Innovation will start again.